The Gradient Particle Magnetohydrodynamics (GPM) algorithm
combines the strengths of an adaptive grid code (AMR) and a
smoothed particle code (SPH) by instilling grid-quality
gradients into a Lagrangian particle code. It is of
particular utility for disk/jet systems.

The hypergradient code uses high-precision tuned finite
differences to achieve spectral-quality resolution with 5
times the speed of a spectral code. The finite differencing
is not based on a high-order polynomial fit. The polynomial
scheme has supurb accuracy for low-wavenumber gradients but
fails at high wavenumbers. We instead use a scheme tuned to
enhance high-wavenumber accuracy at the expense of low
wavenumbers, although the loss of low-wavenumber accuracy is
negligibly slight. A tuned gradient is capable of capturing
all wavenumbers up to 80 percent of the Nyquist limit with
an error of no worse than 1 percent. The fact that gradients
are based on finite differences enables diverse geometries
to be considered and eliminates the parallel communications
bottleneck.

The gravity algorithm is based on the Barnes-Hut tree. It
evades the latencies associated with memory accesses,
divides, and square roots by grouping bundles of particles
together into a simultaneous treewalk and using a polynomial
series to approximate the divides and square roots. The
algorithm runs 10 times faster than the standard tree codes
with no loss of accuracy and it works for individual
timesteps.

If you would like more information about this abstract, please
follow the link to www.alumni.caltech.edu/~maronj/research.html.
This link was provided by the
author. When you follow it, you will leave the Web site for this
meeting; to return, you should use the Back comand on your
browser.